Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  404.10029
Autor:  Erdös, Paul; Sárközy, András
Title:  On differences and sums of integers. I. (In English)
Source:  J. Number Theory 10, 430-450 (1978).
Review:  A set B = {b1,b2,...,bi}\subset{1,2,...,N} is a difference intersector set if for any set A = {a1,a2,...,aj}\subset{1,2,...,N}, j = \epsilon N the equation ax-ay = b has a solution. The notion of a sum intersector set is defined similary. Using exponential sum techniques, the authors prove two theorems which in essence imply that a set which is well-distributed within and amongst all residue classes of small modules is both a difference and a sum intersector set. The regularity of the distribution of the non-zero quadratic residues (mod p) allows the theorems to be used to investigate the solubility of the equations (\frac{ax-ay}p) = +1, (\frac{ar-as}p) = -1, (\frac{at-au}p) = +1, and (\frac{av-aw}p) = -1. The theorems are also used to establish that ''almost all'' sequences form both difference and sum intersector sets.
Reviewer:  M.M.Dodson
Classif.:  * 11B83 Special sequences of integers and polynomials
                   11B13 Additive bases
                   11P99 Additive number theory
                   11D85 Representation problems of integers
                   11L03 Trigonometric and exponential sums, general
Keywords:  difference intersector set; sum intersector set; distribution quadratic residues; sequence of integers

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag

Books Problems Set Theory Combinatorics Extremal Probl/Ramsey Th.
Graph Theory Add.Number Theory Mult.Number Theory Analysis Geometry
Probabability Personalia About Paul Erdös Publication Year Home Page